A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.
Free Semigroup
See also
Free Group, Free Product, SemigroupExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Free Semigroup." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FreeSemigroup.html